A third order of accuracy difference scheme for the Neumann type overdetermined elliptic problem

Abstract

In this paper, a third order of accuracy difference scheme for the approximation of the solution of elliptic identi cation problem with Neumann type overdetermination is presented. We obtain stability estimates for the solutions of constructed difference scheme. Furthermore, a third order of accuracy difference scheme for Neumann type overdetermined multidimensional elliptic problem with Dirichlet boundary condition is constructed. Finally, a numerical example for two-dimensional problem is given.